Elasto-plastic Large Deflection Analysis Research Articles

Lateral Deflection Behavior of Perforated Steel Plates: Experimental and Numerical Approaches

This study aimed to investigate the behavioral characteristics of the lateral deflection of a simply supported perforated steel plate subjected to axial compression. Investigating the lateral deflection of the perforated plate is of great significance because the buckling limit of structural members can be predicted not only by strength but also by displacement (or deflection). For this purpose, we conducted buckling experiments by considering various variables of the perforated plate, such as opening size, thickness, and aspect ratio. In addition, a series of elastoplastic large deflection analyses were performed using the commercial finite element analysis program, and the calculated results were compared along with the experimental results. Finally, practical curves, which can predict lateral deflection with an increase in axial displacement, and the occurrence point of ultimate strength are reported in this study. The results showed that there was a distinct difference in the behavior of lateral deflection between perforated plates with different opening ratios. The local buckling occurred mainly around the opening and was more dominant with an increase in the opening ratio. In addition, the ultimate strength of the perforated plate was determined at the end of the local buckling phase.

Experimental Study and Development of Design Formula for Estimating the Ultimate Strength of Curved Plates

The curved plate has been extensively used as a structural member in many industrial fields, especially the shipbuilding industry. The present study investigated the ultimate strength and collapse behavior of the simply supported curved plate under a longitudinal compressive load. To do this, experimental apparatuses for evaluating the buckling collapse test of the curved plates was developed. Then, a series of buckling collapse experiments was carried out by considering the flank angle, slenderness ratio, and aspect ratio of plates. To examine the fundamental buckling and collapse behavior of the curved plate, elastoplastic large deflection analysis was performed using the commercial finite element analysis program. On the basis of both the experimental and FE analysis, the effects of the flank angle, slenderness ratio, and aspect ratio on the characteristics of the buckling and collapse behavior of the curved plates are discussed. Finally, the empirical design formula for predicting the ultimate strength of curved plates was derived. The proposed empirical formula is a good indicator for estimating the behavior of the curved plate.

Towards a unified formulation for the ultimate strength assessment of uncorroded and pitted platings under uniaxial compression

A benchmark study, devoted to systematically investigate the ultimate strength of simply supported platings under uniaxial compression, is performed to develop unified design formulas, accounting for geometrical imperfections, welding residual stresses and pitting corrosion wastage. Particularly, two boundary conditions for the in-plane motion of longitudinal edges, namely free and fully restrained, are considered as they significantly affect the plating behaviour in the post-buckling regime. Several practical design equations for uncorroded platings are derived to account for different levels of initial deflections and residual stresses, based on a wide and systematic series of elasto-plastic large deflection analyses performed by Ansys Mechanical APDL. Subsequently, proposed formulas are extended to platings affected by pitting corrosion wastage, on the basis of a new series of FE analysis, where the pitting intensity and corrosion degrees are systematically varied based on random distribution of the corrosion wastage on the plate panel. Finally, the goodness of proposed formulas is checked against current Rule equations, as well as several experimental collapse tests and FE results available in literature.

Numerical investigation and development of design formula for cylindrically curved plates on ships and offshore structures

Although guidelines exist for evaluation of the buckling strength of curved plates on ships and offshore structures, they do not reflect the effects of curvature or detail their geometric characteristics. From estimations made using cylinder models, it is known that curvature is expected to increase the buckling strength and the ultimate strength of a curved plate. Therefore, it may be designed accordingly. This study aims to clarify and examine the fundamental behaviour of cylindrically curved plates under axial compression and lateral pressure via a series of elasto-plastic large deflection analyses. On the basis of these results, the effects of curvature, initial deflection, slenderness and aspect ratio, boundary conditions and secondary buckling behaviour are discussed and developed with a modified Faulkner's formula to obtain a double beta formula to predict the ultimate strength of the curved plate.

Development of Design Formula for Predicting Post-Buckling Behaviour and Ultimate Strength of Cylindrical Shell

Cylindrical shells are often used in ship structures at deck plating with a camber, side shell plating at fore and aft parts, and bilge structure part. It has been believed that such curved shells can be modelled fundamentally by a part of a cylinder under axial compression. From the estimations with the usage of cylinder models, it is known that, in general, curvature increases the buckling strength of a curved shell subjected to axial compression, and that curvature is also expected to increase the ultimate strength. We conduct series of elasto-plastic large deflection analyses in order to clarify the fundamentals in buckling and plastic collapse behaviour of cylindrical shells under axial compression. From the numerical results, we derive design formula for predicting the ultimate strength of cylindrical shell, based on a series of the nonlinear finite element calculations for all edges, simply supporting plating, varying the slenderness ratio, curvature and aspect ratio, as well as the following design formulae for predicting the ultimate strength of cylindrical shell. From a number of analysis results, fitting curve can be developed to use parameter of slenderness ratio with implementation of the method of least squares. The accuracy of design formulae for evaluating ultimate strength has been confirmed by comparing the calculated results with the FE-analysis results and it has a good agreement to predict their ultimate strength.

Computational analysis and design formula development for the design of curved plates for ships and offshore structures

In general, cylindrically curved plates are used in ships and offshore structures such as wind towers, spa structures, fore and aft side shell plating, and bilge circle parts in merchant vessels. In a number of studies, it has been shown that curvature increases the buckling strength of a plate under compressive loading, and the ultimate load-carrying capacity is also expected to increase. In the present paper, a series of elastic and elastoplastic large deflection analyses were performed using the commercial finite element analysis program (MSC.NASTRAN/PATRAN) in order to clarify and examine the fundamental buckling and collapse behaviors of curved plates subjected to combined axial compression and lateral pressure. On the basis of the numerical results, the effects of curvature, the magnitude of the initial deflection, the slenderness ratio, and the aspect ratio on the characteristics of the buckling and collapse behavior of the curved plates are discussed. On the basis of the calculated results, the design formula was developed to predict the buckling and ultimate strengths of curved plates subjected to combined loads in an analytical manner. The buckling strength behaviors were simulated by performing elastic large deflection analyses. The newly developed formulations were applied in order to perform verification analyses for the curved plates by comparing the numerical results, and then, the usefulness of the proposed method was demonstrated.

Buckling/ultimate strength and progressive collapse behaviour comparison of unstiffened and stiffened curved plates subjected to axial compression

A ship structure is basically an assembly of stiffened panel elements and an estimation of the maximum load carrying capacity. The ultimate strength of these members is of the highest importance task for the safety assessment and rational design of the structure. In general, cylindrically curved unstiffened and stiffened plates are often used in ship structures, for example at deck plating with a camber, side shell plating at fore and aft parts and bilge circle part. It has been known that curvature increases the buckling strength of a plate subjected to axial compression, and is expected to increase also the ultimate strength. In the present paper, to clarify and examine the fundamental buckling and progressive collapse behaviours of unstiffened and stiffened curved plates subjected to axial compressive load, a series of elastic and elastoplastic large deflection analyses are performed applying non-linear FEM codes, ULSAS and ANSYS. On the basis of the numerical results, influences of curvature, magnitude of initial deflection, slenderness ratio and aspect ratio on the characteristics of the buckling/ultimate strength and progressive collapse behaviour of unstiffened and stiffened curved plates under axial compression are discussed.

Characteristics of Buckling and Ultimate Strength and Collapse Behaviour of Cylindrically Curved Plates Subjected to Axial Compression

In the present paper, to clarify and examine the fundamental buckling behaviours of cylindrically curved plates subjected to axial loading, a series of elastic and elasto-plastic large deflection analyses as well as elastic eigen buckling analysis are performed together with the comparisons with the buckling behaviours of circular cylinder. On the basis of the numerical results, the effects of curvature, magnitude of initial imperfection, slenderness ratio and aspect ratio on the characteristics of the buckling and post buckling collapse behavior of cylindrically curved plates and circular cylinders under axial compression are discussed. The buckling strength and ultimate strength formulae of the cylindrically curved plate are empirically derived based on the FEM series analysis by curve fitting using least square method. The validity of the ultimate strength formulations developed in this study has to some extent been verified through comparison with nonlinear numerical solutions.

압축하중을 받는 유공보강판 구조의 최종강도 설계식 개발

Ship structures are thin-walled structures and lots of cutouts, for example, of inner bottom structure, girder, upper deck hatch, floor and dia-frame etc. In the case where a plate has cutout it experiences reduced buckling and ultimate strength and at the same time the in-plane stress under compressive load produced by hull girder bending will be redistributed. In the present paper, we investigated several kinds of perforated stiffened model from actual ship structure and series of elasto-plastic large deflection analyses were performed to investigate into the influence of perforation on the buckling and ultimate strength of the perforated stiffened plate varying the cutout ratio, web height, thickness and type of cross-section by commercial FEA program(ANSYS). Closed-form formulas for predicting the ultimate strength of the perforated stiffened plate are empirically derived by curve fitting based on the Finite Element Analysis results. These formulas are used to evaluate the ultimate strength, which showed good correlation with FEM results. These results will be useful for evaluating the ultimate strength of the perforated stiffened plate in the preliminary design.

보강판의 해석모델에 따른 좌굴 및 소성거동 평가

선체구조는 기본적으로 판부재의 조합으로 이루어져 있으며, 이러한 판부재의 하중분담 능력 혹은 최종강도 평가는 선체구조의 합리적인 설계 및 구조의 안정성 평가에 있어서는 아주 중요하다. 또한, 선체구조를 구성하고 있는 구조요소들은 작용외력에 대하여 개별적으로 작용하지 않으며 전체적으로 연속거동을 하게 된다. 실제 선박에서의 붕괴형태 중 한가지는 종방향 굽휨에 의해서 갑판 혹은 선저부에 좌굴 및 소성붕괴이다. 그래서, 합리적인 설계에서는 이러한 급작스런 붕괴형태를 방지하기 위하여 좌굴 및 소성붕괴 거동을 파악하는 것이 아주 중요하며, 실제 선박에서는 갑판부와 선저부에서는 하중분담 능력을 증가시키기 위하여 여러개의 종보강재를 가진 보강판 구조의 설계를 하게 된다. 본 연구에서는 선체 판넬구조의 모델링 방법에 따른 최종강도 거동의 차이를 분석하여, 합리적인 모델링영역을 규명하고자 한다. 사용된 해석 모델은 실제 상선의 이중저구조에서 사용되는 판넬에서 채택하였으며 유한요소해석 모델링 시 3가지 단면형상에 대해 각각 6가지 서로 다른 해석모델을 적용하였으며, 이때 보강재의 단면형상을 변화하였다. 본 연구의 목적은 압축하중이 작용하는 선체 보강판구조에서 해석영역에 대한 좌굴 및 최종강도 거동의 특성을 분석하였다. Ship structures are basically an assembly of plate elements and estimation load-carrying capacity or the ultimate strength is one of the most important criterion for estimated safety assessment and rational design on the ship structure. Also, Structural elements making up ship plated structures do not work separately against external load. One of the critical collapse events of a ship structure is the occurrence of overall buckling and plastic collapse of deck or bottom structure subjected to longitudinal bending. So, the deck and the bottom plates are reinforced by a number af longitudinal stiffeners to increase their strength and load-carrying capacity. For a rational design avoiding such a sudden collapse, it is very important to know the buckling and plastic behaviour or collapse pattern of the stiffened plate under axial compression. In this present study, to investigate effect af modeling range, the finite element method are used and their results are compared varying the analysis ranges. When making the FEA model, six types of structural modeling are adopted varying the cross section of stiffener. In the present paper, a series of FEM elastoplastic large deflection analyses is performed on a stiffened plate with fiat-bar, angle-bar and tee-bar stiffeners. When the applied axial loading, the influences of cross-sectional geometries on collapse behaviour are discussed. The purpose of the present study is examined to numerically calculate the characteristics of buckling and ultimate strength behavior according to the analysis method of ship's stiffened plate subject to axial loading.

면내 조합하중과 횡압을 받는 선박 이중판의 강도 평가

A study for the structural strength evaluation of doubler plates subjected to the in-plane combined load and lateral pressure load has been performed through a systematic evaluation process. In order to properly estimate the static strength of doubler plate, elasto-plastic large deflection analysis is introduced including the contact effect between main plate and doubler. The characteristics of stiffness and strength variation are discussed based on the analysis results. Also, in order to compare the doubler structure with the original strength of main plate without doubler, a simple formula for the evaluation of the equivalent flat plate thickness is derived based on the additional series analysis of fiat plate structure. Using this derived equation, the thickness change of a equivalent flat plate is analyzed according to the variation of various design parameters of doubler plate and some design guides are suggested In order to maintain the original strength of main plate without doubler reinforcement. Finally, correlation between derived equivalent plate thickness formula and the developed buckling strength formulas for intact plates by author et al. is discovered and these relations are formulated for the future development of simple strength evaluation formula of doubler plate structure.

Elastoplastic Large Deflection Analysis of Three-Dimensional Steel Frames

A beam element is presented for analysis of the elastoplastic large deflection of three-dimensional (3D) frames that have steel members with semirigid joints. A plastic hinge type formulation was employed, combining the “modified incremental stiffness method,” the updated Lagrangian formulation, and numerical integration about the end sections of the element. The end sections of the element are discretized into small areas to estimate the plastic deformations of the element. The elastic and plastic deformations of the element are treated separately. The behavior of a semirigid joint is modeled as the element-end compliance. The method can treat comprehensively the plastic deformations due to torsion and warping. Considering the assumptions of the method, a four-element approximation for a member gives excellent results for a 3D analysis of semirigid and pin-connected steel frames as well as for rigid frames. The adequacy of the method is verified by comparing the results with experimental ones obtained by the writer. Some examples are presented to demonstrate the accuracy and efficiency of the method.

Study on Buckling/Ultimate Strength of Bilge Circle Part and Its Contribution to Ultimate Hull Girder Strength

There are several methods to estimate the ultimate strength of hull girder, among which the method developed by Smith is widely used as a simple and practical method. In this method, the round corners such as a bilge shell part are usually considered as hard corner elements which do not undergo buckling. A series of elastoplastic large deflection analyses were performed to investigate buckling/plastic collapse behaviour of the bilge circle part subjected to uni-axial thrust. Based on the calculated results, simple formulas were derived to simulate buckling/plastic collapse behaviour of the bilge shell. The ultimate strength analyses of hull girder by Smith's method were carried out taking the buckling/plastic collapse behaviour of the bilge shell into account. Through these studies, it has been found that:(1) A bilge structure with a conventional shape and size reaches the ultimate strength by yielding before buckling takes place. After the ultimate strength has been attained, plastic buckling takes place and the capacity decreases with the increase in deflection.(2) The buckling/ultimate strength of the bilge circle part is dominated by design parameters such as radius/thickness ratio, yield stress and length/radius ratio of the bilge circle part.(3) Hard corner elements could be used for bilge circle part to calculate the ultimate hull girder strength applying the Smith's method.(4) However, the influence of buckling of the bilge circle part has to be taken into account for the accurate estimation of the load carrying capacity beyond the ultimate strength when the Smith's method is applied.

Estimation of buckling and ultimate strength of continuous plate with cutout under thrust

A series of buckling eigen-value calculations and elastoplastic large deflection analyses of simply upported continuous plate with cutout under thrust has been performed. Firstly, simple formulae for estimation of elastic buckling strength have been derived based on the results of eigen-value calculations. Secondary, it has been clarified that the buckling strength evaluated by the existing plastic correction methods exceeds the ultimate strength in some combinations of plate thickness and cutout diameter. So, new plastic correction formula considering the yielding effect for estimation of buckling strength of continuous plate with cutout has been proposed. Finally, by focusing on the characteristics of ultimate strength obtained by elastoplastic large deflection analyses, simple formulae for estimation of ultimate strength of continuous plate with cutout have been derived.

Buckling/Ultimate Strength of Perforated Rectangular Plate under Thrust (2nd Report)

Series of elastic eigenvalue analyses and elastoplastic large deflection analyses were performed to investigate into the influence of perforation on the buckling/ultimate strength of rectangular plate subjected to uni-axial and bi-axial thrust. It has been found that : (1) Beyond the ultimate strength, plastic deformation is concentrated around the opening, and elastic unloading takes place in the remaining part in case of long plate subjected to longitudinal thrust.(2) Beyond the ultimate strength, plastic mechanism of a roof mode developes in case of long plate subjected to transverse thrust.(3) Ultimate strength interaction relationship is derived for bi-axial compression, and it was found that general yielding at the perforated cross-section affects the shape of the interaction curve.Simple formulas are proposed to evaluate the elastic buckling strength of a perforated plate under uni-axial thrust. These formulas are used to evaluate the ultimate strength, which showed good correlations with the FEM results.

Elasto-plastic response of uniformly loaded sector plates: full-section yield model predictions and spread of plasticity

The governing equations for an elasto-plastic large deflection analysis of pressure loaded sector plates, based on the Ilyushin full-section yield criterion and the flow theory of plasticity, are presented. An outline of the solution of these equations using a finite difference implementation of the dynamic relaxation algorithm is given. Numerical results are presented for uniformly loaded slender and stocky sector plates with a 60° sector angle. In particular, first yield data are presented as well as the results of two parameter studies. The first study shows the effects of flexural and in-plane edge conditions on the deflections and stress resultants/couples at the centre of the sector plate and the second contrasts the spread of plasticity in slender sector plates with simply supported and clamped in-plane fixed edges.

Estimation of buckling and ultimate strength of rectangular plate with cutout

A series of buckling eigen-value calculations and elastoplastic large deflection analyses of simply supported rectangular plate with cutout subjected to in-plane loads has been performed. Firstly, advanced simple formulae in practical use for estimation of elastic buckling strength have been derived based on the results of eigen-value calculations. Secondary, relationship between the ultimate strength and the buckling strength evaluated by the existing plastic correction methods has been clarified. By considering the yielding in the effective cross section with cutout, new plastic correction formula for estimation of plastic buckling strength of rectangular plates with cutout has been proposed. Finally, based on the results of elastoplastic large deflection analyses, simple formulae for estimation of ultimate strength of rectangular plate with cutout subject to longitudinal thrust have been derived.

Buckling/Ultimate Strength of Perforated Rectangular Plate under Thrust

A series of elastoplastic large deflection analyses was performed to investigate into the influence of perforation on the buckling and ultimate strength of rectangular plate under uni-axial thrust. It has been found that : (1) When the plate is subjected to longitudinal thrust, collapse mode varies depending on the aspect ratio of the plate and sometimes differs from the elastic buckling mode.(2) When the plate is subjected to transverse thrust, collapse mode is fundamentally the same regardless of the aspect ratio and is almost the same as the elastic buckling mode.(3) Simple formulas are proposed to evaluate the ultimate strength of a perforated plate under uni-axial thrust both in longitudinal and transverse directions. The evaluated values of the ultimate strength showed good correlations with the FEM results.

Plastic Collapse Strength of Hatch Cover of Bulk Carrier against Green Sea Load (1st Report)

After the casualty of M.V.Derbyshire, United Kingdom insisted to increase the strength of a hatch cover of a Bulk Carrier to prevent the occurrence of similar casualties. This had been discussed at the International Association of Classification Societies (IACS), and a new unified rule, S21, came into effect. In the present paper, elastoplastic large deflection analysis is performed on two hatch covers of a folding type designed by the old rule in the International Convention on Load Lines (ICLL), 1966 and the new IACS rule, respectively. Based on observations on the simulated collapse behaviour by FEM, a simplified method is proposed to evaluate the plastic collapse strength of a hatch cover of a folding type. It is demonstrated that the proposed method gives accurate collapse load. At the end, strength of old and new hatch covers are assessed comparing the evaluated collapse strength with design loads specified by the rules. It is concluded that the hatch cover designed by the new IACS rule has appropriate and enough strength.

A numerical investigation of tripping

The twin aims of the present study are to investigate numerically the characteristics of tripping failure of flat-bar stiffened panels subject to uniaxial compressive loads and also to study the accuracy of two available design formulations. A special-purpose nonlinear finite element method capable of efficiently analyzing the elasto-plastic large deflection behavior of stiffened panels is developed and used in the study. A benefit of the application of the nonlinear finite element method is that it makes possible a rigorous accounting of the interacting effects of stiffener tripping and plating collapse and also the inclusion of the influence of elasto-plastic rotational restraint at the plate-stiffener intersection prior to and during failure. A parametric series of elasto-plastic large deflection analyses for stiffened panels with flat-bar type of stiffeners under uniaxial compressive loads are carried out varying member proportions and structural parameters. Based on the computed results, a basic investigation of tripping behavior of flat-bars is made, and the accuracy of design formulations is studied. The calculations and comparisons of this paper are for flat-bar stiffened panels under uniaxial compression, but the special-purpose finite element method implemented is considerably more general.